Abstract. According to legend, the gods of ancient Greece drowned the Pythagorean philosopher Hippasus for the heresy of proving the existence of irrational numbers through the square root of 2. Taking this heresy further, I will talk about the transcendental numbers, which are the numbers that solve no polynomial equation with rational coefficients. It is today well-known that almost all real numbers are transcendental, yet their existence was not proven until the mid-19th century. I will give special attention to the exponential function, which turns out to be an excellent source of transcendental numbers and even provided the first proof of the transcendence of π.